Types of Numbers

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

Natural numbers (1, 2, 3, ...) are for counting. Adding 0 gives whole numbers; adding negatives gives integers (..., -2, -1, 0, 1, 2, ...).

Q = {p/q : p, q integers, q not 0}. Every integer counts (n = n/1). Decimals that stop (0.75 = 3/4) or repeat (0.333... = 1/3) are rational too.

sqrt(2), sqrt(3), pi and e are irrational. sqrt(n) is irrational unless n is a perfect square.

The reals (R) are every point on the line. Rationals leave tiny gaps; irrationals fill exactly those gaps.

Natural numbers	The positive counting numbers 1, 2, 3, ...
Whole numbers	The natural numbers together with 0.
Integer	Any whole number, positive, negative or zero.
Rational number	A number expressible as p/q where p, q are integers and q is not 0.
Irrational number	A number that cannot be written as p/q; its decimal is non-terminating and non-recurring.
Terminating decimal	A decimal that ends after finitely many digits, e.g. 0.25.
Recurring decimal	A decimal with a block of digits repeating forever, e.g. 0.142857...
Surd	An irrational root such as sqrt(2) or sqrt(3) left in root form.

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